en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{4}(sqrt(64))

Solution

simplify

lo g_{4} (64)

Solution

\frac{3}{2}

+1

Solution steps

lo g_{4} (64)

Factor the number:

4 = 2^{2}

= lo g_{2^{2}} (64)

Apply log rule:

lo g_{a^{b}} (x) = \frac{1}{b} lo g_{a} (x), a > 0

lo g_{2^{2}} (64) = \frac{1}{2} lo g_{2} (64)

= \frac{1}{2} lo g_{2} (64)

64 = 2^{3}

= \frac{1}{2} lo g_{2} (2^{3})

Apply log rule:

lo g_{a} (a^{b}) = b

lo g_{2} (2^{3}) = 3

= \frac{1}{2} \cdot 3

\frac{1}{2} \cdot 3 = \frac{3}{2}

= \frac{3}{2}

Popular Examples

3 (x - 4) = 1 - 2 x + 7

simplify 7/3-1 simplify

\frac{7}{3} - 1

factor 9b^2-1 factor

9 b^{2} - 1

factor (5x^2+2x)+(10x+4)factor

(5 x^{2} + 2 x) + (10 x + 4)

factor 1-1/8 p^3 factor

1 - \frac{1}{8} p^{3}

Frequently Asked Questions (FAQ)

What is log_{4}(sqrt(64)) ?
The solution to log_{4}(sqrt(64)) is 3/2